Francesco De Santis — Università di Roma "La Sapienza" #
Numerical Computation of the Bethe Lattice Spin Glass order parameter at Zero Temperature #
The Bethe Lattice spin glass is a system with finite connectivity whose low temperature phase is believed to be described by full Replica Symmetry Breaking (RSB). The computation of the order parameter is a valid tool of investigation into the properties of the RSB phase. Although an analytical approach is only possible in a limited class of mean field systems, a numerical computation is still possible. We rely on a general formula which holds for systems in the RSB phase, which exploits the information coming from the probability distribution of the lowest lying states. The latter is computed numerically by applying a convenient perturbation to the hamiltonian and considering the distribution of the overlap between the original and the perturbed ground state.